To effetuate addition or subtraction of polynomials, we just have to realize the operation with the coefficients of the corresponding degree.
[tex]\begin{gathered} P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_2x^2+a_1x+a_0 \\ Q(x)=b_nx^n+b_{n-1}x^{n-1}+...+b_2x^2+b_1x+b_0 \\ P(x)-Q(x)=(a_n-b_n)x^n+(a_{n-1}-b_{n-1})x^{n-1}+...+(a_2-b_2)x^2+(a_1-b_1)x+(a_0-b_0) \end{gathered}[/tex]Then, performing the given operation, we have:
[tex]\begin{gathered} (6x^5+3x^3-2)-(2x^5-6x^3+7) \\ =6x^5+3x^3-2-2x^5+6x^3-7 \\ =(6-2)x^5+(3-2)x^3+(-2-7) \\ =4x^5+x^3-9 \end{gathered}[/tex]Thus, this is our answer
[tex](6x^5+3x^3-2)-(2x^5-6x^3+7)=4x^5+x^3-9[/tex]
